Conway type invariants of links and Kauffman's method
Abstract
In this chapter (Chapter III) we introduce the concept of Conway algebras (the notion related to entropic magmas) and describe invariants of links yielded by (partial) Conway algebras (including the Homflypt polynomial and signatures). We present, in detail, a proof (following the original Przytycki-Traczyk 1984 proof) of the existence of Conway type invariants. Then we describe Kauffman's method of constructing link invariants, in particular, giving the Kauffman polynomial of two variables. We develop a formalism, Kauffman algebras, analogous to that of Conway algebras. This chapter, along with chapters II, IV, and V of the book (already on arXiv), form the core of the first part of the book.
Keywords
Cite
@article{arxiv.1209.1592,
title = {Conway type invariants of links and Kauffman's method},
author = {Jozef H. Przytycki},
journal= {arXiv preprint arXiv:1209.1592},
year = {2012}
}
Comments
109 pages, 82 figures, Chapter III of the book "KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots"